THE CLASSIFICATION AND PERIOD OF STATES FOR MARKOV CHAIN IN RANDOM ENVIRONMENT

This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced and it is obtained that the period is a “class property” ,i.e. two states x and y belong to same class implies the period of x is equal to the period of y.     

ΓD‐convergence for a class of quasilinear elliptic equations in thin structures

We study the asymptotic behaviour of the solution of a stationary quasilinear elliptic problem posed in a domain Ω^(ε) of asymptotically degenerating measure, i.e. meas Ω^(ε) → 0 as ε → 0, where ε is the parameter that characterizes the scale of the microstructure. We obtain the convergence of the solution and the homogenized model of the problem is constructed using the notion of convergence in domains of degenerating measure. Proofs are given using the method of local characteristics of the medium Ω^(ε) associated with our problem in a variational form. Copyright © 2005 John Wiley & Sons, Ltd.     

Analytic Feynman integrals of transforms of variation of cylinder type functions over Wiener paths in abstract Wiener space

In this paper, we evaluate various analytic Feynman integrals of first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of cylinder type functions defined over Wiener paths in abstract Wiener space. We also derive the analytic Feynman integral of the conditional Fourier-Feynman transform for the product of the cylinder type functions which define the functions in a Banach algebra introduced by Yoo, with n linear factors.     

Influence of radiation on thin ZnS-Tb films

Changes in thin zinc-sulfide films under the action of the γ-radiation of Co⁶⁰ are studied by investigating electroluminescence spectra of terbium embedded in these films as a luminescent probe. It is shown that changes in the relation of the intensities of bands, a decrease in their halfwidth and the background component, and simplification of the spectrum are observed in a short-wave region of the Tb radiation spectrum that corresponds to⁵D₃→⁷F_j transitions. The same modification of the radiation spectrum is characteristic of ZnS films whose crystalline structure is ordered in the course of thermal annealing at a temperature of 350°C. Based on the analysis of the data obtained it is inferred that irradiating the ZnS films with small radiation doses of 10⁴–10⁵ rad leads to the ordering of their crystalline structure due to the elimination of one of the types of structural defects. Institute of Physics of Semiconductors, National Academy of Sciences of Ukraine, 45, Nauka Ave., Kiev-28, 252650. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 3, pp. 338–341, May–June, 1997.     

Luminescence properties of anodic aluminum oxide films with organic luminophores embedded into pores

Luminescence properties of porous anodic aluminum oxide films formed in a 0.6 M solution of citric acid and luminescence of paraterphenyl, perylene, coumarin 7, and rhodamine 6G dyes adsorbed by the films are investigated. The nature of emitting centers in anodic aluminum oxide is revealed. Intense photoluminescence of all tested dyes embedded into pores of anodic aluminum oxide has been found. A redshift of fluorescence spectra of dyes adsorbed by the matrix and emergence of an additional longwave band have been detected. Data obtained can be used in developing new thin-film luminescent coatings for future applications in optoelectronics and molecular electronics. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No 4, pp. 483–488, July–August, 1997.     

LB膜混合聚集体中极性基团相互作用对光学非线性的影响

通过紫外－可见吸收光谱、压力－面积等温线、二次谐波的测量，研究了不同活性分子混合聚集体的形成对ＬＢ膜光学性质的影响。分子极性基团间的相互作用，使激发态能量及平均偶极矩发生变化，导致ＬＢ膜的光学非线性明显地增强或减弱。     

Differentiability of the Value Function of Nonclassical Optimal Growth Models

We consider an optimal growth (multi-sector) model with nonconvex technology. Using the Clarke results on generalized gradients, we prove that the value function has left and right derivatives with respect to the initial capital stock, without requiring supermodularity assumptions.     

Forced-air precooling of spherical foods in bulk: A parametric study

In this paper, a mathematical model for forced-air precooling of spherical food products in bulk is developed. The foods are arranged in horizontal layers stacked one above the other to form a rectangular parallelepiped with a vertical gap in between the product layers. The foods are cooled by chilled air blown along the height of the package. The governing equations for the conduction heat transfer in the foods, simultaneous heat and mass transfer at the food-air interface and in the air stream are solved numerically using finite-difference methods. A comprehensive numerical study is performed by varying the process parameters over a wide range. Typical results showing the variation of moist air properties along the height of the package and the effect of each parameter on the process time are presented. The ranges of parameters for advantageous operation of the precooling system are identified. Correlations are obtained for the process time based on the product center and mass-averaged temperatures in terms of process parameters.     

Novel pattern formation in the collapse process of floating monolayer at the air-water interface

We have observed a remarkable two-armed spiral in the collapse process of a floating monolayer at the air-water interface by phase contrast microscopy. This demonstrates that the floating monolayer as a form of soft condensed matter reorganizes itself due to a certain kind of macroscopic or collective behavior of molecules as it collapses. This pattern formation is caused by the breakdown of a critical dynamical balance between the deformation of solid domain and the applied surface pressure. The fragility as well as the flexibility of the floating monolayer can be associated with the observed pattern growth. There are also observed interesting, periodically arranged collections of molecules in numerous collapsed regions. Received: 8 July 1997 / Accepted: 4 November 1997     

Probability relations involving several subsystems

We consider the question of factorizability in tensor product spaces, and argue that the correlations associated with entangled states are even more problematic in the general case involving any tensor product of Hilbert spaces, than in the Einstein, Podolsky, and Rosen case with only two [1].